Why do rigidbodies snap back when keying "animated"?
The only way I can get  the effect you describe is when the objects are following the path directly.

When the physics is switched on by unticking the Animated box, we'd have two functions wrestling to control the same object and clearly they don't get along.
The usual way around this is to use an empty to follow the path and parent the object to that.  The physics will then be free of interference when the Animated box is keyframed off.

If I've misunderstood your query, leave a comment and I'll delete it.